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Technical Studies Reference


Standard Error Bands

This study calculates and displays Standard Error bands for the data specified by the Input Data Input. This study is similar in appearance to Bollinger Bands, however they are calculated and interpreted differently. Where Bollinger Bands are plotted at Standard Deviation levels above and below a Moving Average, Standard Error Bands are plotted at Standard Error levels above and below a Linear Regression Indicator.

Let \(X\) be a random variable denoting the Input Data, and let \(X_t\) be the value of the Input Data at Index \(t\). Let the Inputes Length and Standard Deviations be denoted as \(n\) and \(v\), respectively. The Standard Error for the given Inputs at Index \(t\) is denoted as \(SE_t(X,n)\), and we calculate it for \(t \geq n - 1\) as follows.

\(\displaystyle{SE_t(X,n) = \sqrt{\frac{\sum_{k = 0}^{n - 1}\left(X_{k + t - n + 1} - MA_t(X,n)\right)^2 - \left(\sum_{k = 0}^{n - 1}\left(k - \frac{n - 1}{2}\right)\left(X_{k + t - n + 1} - MA_t(X,n)\right)\right)^2}{(n - 2)\sum_{k = 0}^{n - 1}\left(k - \frac{n - 1}{2}\right)^2}}}\)

There are three Standard Error Bands. The middle band is just the Linear Regression Indicator \(LRI_t(X,n)\). The Top and Bottom Bands for the given Inputs at Index \(t\) are denoted as \(TB^{(SE)}_t(X,n)\) and \(BB^{(SE)}_t(X,n)\), respectively, and we compute them for \(t \geq n - 1\) as follows.

\(TB^{(SE)}_t(X,n) = LRI(X,n) + v\cdot SE_t(X,n)\)
\(BB^{(SE)}_t(X,n) = LRI(X,n) - v\cdot SE_t(X,n)\)

Inputs

Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through File >> Open Spreadsheet.

Standard_Error_Bands.103.scss


*Last modified Thursday, 13th September, 2018.